Question

Решить неравенства по примеру на фото
б) -12 < 5 - х < 17;
г) -1 < 5у + 4 < 19.​

Answer 1

$1)-12<5-x<17\\\\\left \{ {{5-x>-12} \atop {5-x<17}} \right.\\\\\left \{ {{-x>-12-5} \atop {-x<17-5}} \right.\\\\\left \{ {{-x>-17} \atop {-x<12}} \right.\\\\\left \{ {{x<17} \atop {x>-12}} \right.$

\\\\\\\\\\\\\\\\\\\\\\\\\\\

______₀_______₀_______

          - 12             17

             /////////////////////////////

Ответ : (- 12 ; 17)

$2)-1<5y+4<19\\\\\left \{ {{5y+4>-1} \atop {5y+4<19}} \right. \\\\\left \{ {{5y>-1-4} \atop {5y<19-4}} \right.\\\\\left \{ {{5y>-5} \atop {5y<15}} \right.\\\\\left \{ {{y>-1} \atop {y<3}} \right.$

            /////////////////////////////

______₀_______₀_______

           - 1              3

\\\\\\\\\\\\\\\\\\\\\\\\\\\

Ответ : (- 1 ; 3)